Graph details

Graph # 45681

Adjacency matrix

[Too large to display]

Adjacency list

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HoG graph id


Graph name


Graph submitted by

Mikhail Lavrov

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3
Algebraic Connectivity 0.144 Laplacian Largest Eigenvalue 5.562
Average Degree 3 Longest Induced Cycle 4
Bipartite No Longest Induced Path 6
Chromatic Index 4 Matching Number 7
Chromatic Number 3 Maximum Degree 3
Circumference 5 Minimum Degree 3
Claw-Free No Minimum Dominating Set 4
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 24
Density 0.2 Number of Triangles 6
Diameter 6 Number of Vertices 16
Edge Connectivity 1 Planar Yes
Eulerian No Radius 3
Genus 0 Regular Yes
Girth 3 Second Largest Eigenvalue 2.856
Hamiltonian No Smallest Eigenvalue -2.562
Independence Number 7 Vertex Connectivity 1

A table row rendered like this indicates that the graph is marked as being interesting for that invariant.


Posted by Mikhail Lavrov at Aug 24, 2021 8:18 PM.
Smallest cubic graph with no perfect matching. (By a theorem of Petersen, such a graph must have at least three bridges.) Sometimes attributed to Sylvester.

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